The present invention relates to a method for the automatic positioning of a vessel, by which the vessel can be moved, by propulsion means, in the direction opposite of the main external disturbance, or position deviation, forces. And more particularly, the present invention relates to an improved thruster allocation logic for automatic positioning of the vessel, and specifically, to applying numerical optimization methods to the problem of force and moment allocation in vessel position and rate control.
In order to perform the dynamic positioning of the vessel there must be provided propulsion means, which act to hold the vessel accurately at a working position. Proper commands to the propulsion means must be determined with a combination of control laws and thruster allocation logic. Examples of the types of vessels involved are aircraft, spacecraft, submarines, surface ships, and other such vessels. The propulsion means include jet propulsion, rocket propulsion, propellers, adjustable propellers, screws and rudders. It is also possible to combine transverse thrust systems with active propellers.
When a vessel is being dynamically positioned, the vessel is frequently placed with its bow facing in the direction of the resultant of the disturbance forces since in this position it will have the lowest wind, water and/or wave resistance, i.e. the external influences will apply the lowest force levels to the vessel. Another method for setting the required vessel heading is described in U.S. Pat. No. 4,089,287 to Kranert, et al., which discloses an automatic method and apparatus for setting the required vessel heading to minimize the influence of external disturbance forces. Position or rate control of such vessels as aircraft, surface ships, underwater vehicles and rockets has been achieved using a variety of control laws including Proportional/Integral/Derivative, H-infinity, and nonlinear sliding mode controls. All control laws have common inputs and outputs. FIG. 1 illustrates the basic components and relationships involved in current state of the art vessel position control. Desired Position Command Source 101, generates the required vessel positions. The required position inputs can come from an operator, an automatic path planner, or other external sources. Inputs to the Control Laws Logic 102 include required position or rate for the degrees of freedom to be controlled. The other required input to the control laws is feedback on the state of the vessel from Position/Rate Measurement 108, such as Differential Global Positioning Systems, hydro-acoustic positioning systems, and Kalman filters.
Outputs of the Control Law 102 logic are the force or moment in the controlled degree of freedom required achieving the desired position or rate. These forces and moments are usually generated without regard to the vessel""s capability to generate them. Output of External Forces Detector 103, for determining disturbing forces and moments, may supplement the required control forces and moments in a Feed Forward 104. Examples of disturbing forces include, but are not limited to wind, wave, current, gravity and manual thruster commands, and may be detected with a variety of sensors and operator inputs. The Feed Forward 104 may be simply accomplished by addition of forces and moments that compensate for the disturbing forces and moments to the required Control Laws 102 forces and moments via electrical circuit or numerically in a computer. These disturbing forces are detected by sensors and/or inputted to the computer by an operator. The combination of Control Law 102, External Forces 103, and Feed Forward 104 comprise force setting means and moment setting means. The total required forces and moments are then allocated to the available effectors in Thrust Allocation Logic 105 before commands pass to the Force Generating Effectors 106, which generate forces and turning moments that act on Vessel 107.
Until now, the allocation of the forces and moments required to control vessel position to the available vessel Force Generating Effector 106, such as thrusters and rudders, has been synthesized with complicated, highly structured logic. Each new configuration of effectors has required customization of computer software to calculate the best set of commands to the effectors that achieve the required forces and moments on the vessel while observing constraints on the effectors and power availability. Often, there is an infinite number of possible effector command sets that can achieve the required net forces and moments on the vessel. Conventional Thrust Allocation Logic methods do not always select the optimal solution. In some cases, no command set is found that achieves the required forces and moments and the vessel position control is compromised. This may be due to physical limitations of the available effectors or due to failure of the Thrust Allocation Logic to find an existing feasible set.
The set of required forces and moments determined by the Control Laws Logic 102 and Feed Forward 104 can usually be achieved in more than one way. Consider a relatively simple system of a surface ship with two main longitudinal propellers each with its own rudder. There are four independent commands to be determined, one for each effector. Suppose that only three degrees of freedom are to be controlled: fore/aft, port/starboard, and heading. The sum of forces from the two main props must equal the required fore/aft force (ignoring drag forces on the rudders). Rudders acting in the flow of the main propellers must provide the required port/starboard force. The moment required to control heading must be met by the differential forces of the main propellers acting across their lateral (port/starboard) separation plus the moment due to the rudders and their longitudinal (fore/aft) separation from the vessel center of rotation. The four unknowns (commands) are therefore under-specified by the three governing equations.
In some vessel configurations, a fourth equation can be specified, such as a requirement to minimize thruster power, and the four equations are solved simultaneously to determine the necessary effector commands. This is satisfactory only if the fourth equation is the appropriate one for the application and the resulting set of equations can be solved, but that is often not the case. In general, the goals for the allocation of control forces do not lend themselves to simple mathematical solution.
In addition to meeting the required set of control forces, there are frequently other allocation goals to be achieved. These goals include: minimum change from current set of commands; minimum power usage; minimize the maximum effector command; minimize the sum of the squares of the effector commands; minimize the difference between the minimum and the maximum effector commands; and establish preferences for use of one set of effectors over another set.
If the required set of control forces can not be achieved, then it may be desirable to come as close as possible to such control forces, sacrificing control in some degrees of freedom in favor of others. While maximizing performance goals, or minimizing penalties, there may be allocation constraints on the solution. They can be equality constraints or inequality constraints, and they can be linear or nonlinear in the control variables. The most obvious constraints are simple bounds on the allowable commands. Other constraints on an individual effector might include: minimum levels, due to clutching, stiction, or other mechanism; unallowable command regions, such as thruster wash angles spoiling hydrophone sensors or other thrusters, critical shaft speed avoidance, etc.; and minimum thruster level to reduce azimuth control chattering.
Other constraints affect multiple effectors simultaneously, such as maximum total power levels and minimum total power levels required, for example, to meet minimum generator power loading. The requirement to meet the required control forces may also be considered a constraint on the solution set.
Typical of the state of the art in force and moment allocations for disturbing forces for vessels is U.S. Pat. No. 4,532,877 to Nagata, et al., entitled, xe2x80x9cManeuvering System of Watercraft and the Like.xe2x80x9d Nagata, et al. solves a set of simultaneous equations defining the calculation of net forces and moments in surge, augmented by a requirement to minimize the sum of squares of the individual thrusters"" surge and sway force components. Nagata, et al. then describes a method of selecting the minimum reduction of forces required to bring all the thruster commands within their thrust capabilities. All thruster commands are then reduced by this single percentage. The method described by Nagata, et. al. does result in thruster commands that fall within the constraints of thruster capabilities. It does so while maintaining the same ratios of surge, sway, and yaw. In most marine related applications, however, achieving the required yaw moment is given highest priority at the expense of surge and sway forces. Vessel heading is normally oriented into the weather along the vessel""s most streamlined direction so that required control forces are minimized. If the vessel is unable to achieve required control forces in all three degrees of freedom, yaw moment should receive the highest priority since failure in that degree of freedom causes the vessel to rotate perpendicular to the weather making it even more difficult to recover. The method described by Nagata et. al. also fails to achieve the required net thrust force and moment results if any thruster command initially exceeds its rated capability even when some other combination of thruster commands could achieve the required set of forces and moment.
One common method of thrust allocation logic is often referred to as the Pin Wheel Moment allocation because of the pin wheel shape generated in vector diagrams of the resulting effector command. The simultaneous equations are solved with the added constraints that each effector will use the same fraction of rated control force in a given degree of freedom. For example, each thruster might use 25% of its rated surge force capability to meet the total required surge force, 30% of its rated sway force capability to meet the total required sway force, and 45% of its rated moment generating capability to achieve the required yaw moment.
Other methods in use or considered include: assignment of effectors to single degrees of freedom; allocation to meet surge, then sway, then yaw with each allocation adding to the previous one; and table lookup. However, each of these methods has inadequacies which result in the deficiencies noted above.
In the automatic positioning system of the preferred embodiments of the present invention, the Contol Law 102, Feed Forward 104 and Thrust Allocation Logic 105 functions are accomplished in a computer, while the Command Source 101, External Forces 103, Effectors 106, and Feedback Measure 108 are accomplished utilizing manual input, sensors, and electrical and mechanical devices. It is an object of the present invention to provide an improved and new method for positioning a vessel, as described in FIG. 1, using numerical optimization techniques heretofore not used in Thrust Allocation Logic 105, which optimization techniques satisfy all of the constraints on the effector command solution and maximize given performance measurements. This, and other objects, are accomplished according to the present invention by applying numerical optimization methods to the problem of force and moment allocation in vessel position and rate control. Numerical optimization methods have, heretofore, never been applied to Thrust Allocation Logic 105 in vessel control. Numerical optimization methods improve the allocation of effector commands in terms appropriate to the application, often finding solutions not found by current methods, and simplifies the design of new allocation systems. Although the present invention applies to all of the types of vessels as described above, the invention will be described as it relates to a surface ship.
Optimization, in general, is the process of finding a set of independent values that minimize or maximize a set of dependent values in a function. When the dependent values are linearly related to the independent values, linear programming techniques can be applied. In the more general case of nonlinear functions, search techniques are applied depending on the form of the function, the constraints on the independent values, solution time limits, and accuracy requirements. An example of an algorithm applicable to the constrained, nonlinear functions typical of many vessel force and moment allocation problems is sequential quadratic programming. The processing times and memory capabilities of existing computer systems make the trial and error searches of numerical optimization techniques feasible in real time settings.